Membrane potentials, calculation

Membrane permeability for the Cl ions is not in contrast to the conclusion that a simple membrane equilibrium such as that described in Section 5.4.1 is established at the membrane. In fact, the membrane potential calculated for the example above with Eq. (5.26) from the Cl ion concentration ratio is exactly -90mV (i.e., the d ions in the two solutions are in equilibrium, and there is no unidirectional flux of these ions). 

Assuming that 3 H are transported per ATP synthesized in the mitochondrial matrix, the membrane potential difference is 0.18 V (negative inside), and the pH difference is 1 unit (acid outside, basic inside), calculate the largest ratio of [ATP]/[ADP] [P,] under which synthesis of ATP can occur. 

The transmembrane potential derived from a concentration gradient is calculable by means of the Nemst equation. If K+ were the only permeable ion then the membrane potential would be given by Eq. 1. With an ion activity (concentration) gradient for K+ of 10 1 from one side to the other of the membrane at 20 °C, the membrane potential that develops on addition of Valinomycin approaches a limiting value of 58 mV87). This is what is calculated from Eq. 1 and indicates that cation over anion selectivity is essentially total. As the conformation of Valinomycin in nonpolar solvents in the absence of cation is similar to that of the cation complex 105), it is quite understandable that anions have no location for interaction. One could with the Valinomycin structure construct a conformation in which a polar core were formed with six peptide N—H moieties directed inward in place of the C—O moieties but... 

A breakthrough in cell modelling occurred with the work of the British scientists. Sir Alan L. Hodgkin and Sir Andrew F. Huxley, for which they were in 1963 (jointly with Sir John C. Eccles) awarded the Nobel prize. Their new electrical models calculated the changes in membrane potential on the basis of the underlying ionic currents. 

In contrast to the pre-existing models that merely portrayed membrane potentials, the new generation of models calculated the ion fluxes that give rise to the changes in cell electrical potential. Thus, the new models provided the core foundation for a mechanistic description of cell function. Their concept was applied to cardiac cells by Denis Noble in 1960. 

We shall write (p) and (q) for the membrane surface layers adjacent to solutions (a) and (p), respectively. Using the equations reported in Section 5.3, we can calculate the ionic concentrations in these layers as well as the potential differences and between the phases. According to Eq. (5.1), the expression for the total membrane potential additionally contains the diffusion potential within the membrane itself, where equilibrium is lacking. Its value can be found with the equations of Section 5.2 when the values of and have first been calculated. 

Another situation is found for the Na+ ions. When the membrane is permeable to these ions, even if only to a minor extent, they will be driven from the external to the internal solution, not only by diffusion but when the membrane potential is negative, also under the effect of the potential gradient. In the end, the unidirectional flux of these ions should lead to a concentration inside that is substantially higher than that outside. The theoretical value calculated from Eq. (5.15) for the membrane potential of the Na ions is -1-66 mV. Therefore, permeabihty for Na ions should lead to a less negative value of the membrane potential, and this in turn should lead to a larger flux of potassium ions out of the cytoplasm and to a lower concentration difference of these ions. All these conclusions are at variance with experience. 

Before trying to interpret this partial inhibition of S by PCP, we need to consider the influence of membrane potential on the 86Rb efflux. To obtain information about the relationship between component S and membrane potential, we measured S (increase in the slope of 86Rb efflux between 2 and 4 seconds) as a function of [K]0 in the efflux solution, in the absence of drug. These data are shown in figure 3 (solid circles) the calculated depolarization, due to increasing [K]0, is given in the upper abscissa seale. 

When the expressions (6.2.5) are substituted into the Henderson equation (2.5.34) A0l is obtained. Both contributions A0D are calculated from the Donnan equation. From Eq. (6.2.3) we obtain, for the membrane potential,... 

Equilibrium potentials calculated at 37°C from the Nernst equation. Calculated assuming a —90 mV resting potential for the muscle membrane and assuming that chloride ions are at equilibrium at rest. 

In a separate experiment, interfering ions are successively added to an identical reference solution until the membrane potential matches the one obtained before with the primary ion. The selectivity is calculated from the following equation ... 

The action of so-called active transport, also known as ion pumps, facilitates larger Na" /K" gradients than those possible considering calculations of Donnan equilibria. For instance, the concentration of K+ in red blood cells equals 92 mM versus 10 mM in blood plasma. Calculation of the membrane potential using equation 5.11 would lead to a large negative potential ... 

Consider a system in which the analyte contains both determinand J and interferent K, and where a diffusion potential is formed in the membrane as a result of their different mobilities. A simplification that provides the basic characteristics of the membrane potential employs the Henderson equation for calculation of the diffusion potential in the membrane. According to (2.1.9) the membrane potential is separated into three parts, two potential differences between the membrane and the solutions A 0 and Aq with which it is ip contact, and the diffusion potential inside the membrane... 

Finally, the result of a theoretical treatment of a similar system with almost complete association in the membrane will be given without calculations [66,67]. The diffusion potential in the membrane depends not only on electrodiffusion of J, and A but also on diffusion of associates JA and KA. The resultant formula for the membrane potential is... 

Finally, in 3.4 we present a calculation of membrane potential in terms of the classical Teorell-Meyer-Sievers (TMS) [2], [3] model of a charged permselective membrane. In spite of its extreme simplicity, this calculation yields a practically useful result and is typical for numerous membrane computations, some more of which will be touched upon subsequently in Chapter 4. 

Below we present a well-known calculation of membrane potential based on the classical Teorell-Meyer-Sievers (TMS) membrane model [2], [3]. The essence of this model is in treating the ion-selective membrane as a homogeneous layer of electrolyte solution with constant fixed charge density and with local ionic equilibrium at the membrane/solution interfaces. In spite of the obvious idealization involved in the first assumption the TMS model often yields useful results and represents in fact the main tool for practical membrane calculations. We shall return to TMS once again in 4.4 when discussing the electric current effects upon membrane selectivity. In the case of our present interest, the simplest TMS model of membrane potential for a 1,2 valent electrolyte reads... 

For the calculation of membrane phenomena as diffusion through membranes, membrane potentials, electrical resistance, transference numbers during electrodialysis, concentration profiles in the membrane under different circumstances, the flux equations have to be solved with the appropriate boundary-conditions. 

The concentration of all ions in the two surface layers in the membrane are considered to be given. These are related to those of the outer solution by a set of Donnan relations analogous to equation (24). Schlogl calculated the fluxes, the profiles of the concentrations in the membrane and the membrane potential. 

Influence of unstirred layers near the membrane. Near the membrane there exist unstirred layers which under unfavourable conditions can exert a considerable influence on the fluxes and the membrane potential too. F. Helfferich (57) has drawn the attention to this effect. The thickness of these layers depends on the rate of stirring. Under good stirring conditions the film-thickness amounts to 20 to 1 10-3 cm. Under extreme conditions it can be reduced to 10-4 cm. It is not always possible to eliminate its influence (139). The transport in the films is diffusion-controlled. In some cases the effect of the films can be involved in the calculations. As an example the case of selfdiffusion is given here. A cation-exchange resin separates two solutions of identical chemical composition. The cations on either side are isotopes of the same element. 

For the calculation of the membrane potential EM with the aid of (39), the transference numbers and the activities of the ions in each place in the membrane must be known. However, in general this is not the case. 

Bi-Ionic Potentials (B.I.P s). If a membrane separates two salt solutions with two different counterions, but the same co-ion, the corresponding membrane potential is called bi-ionic potential. For the calculation of the B.I.P. this is split in a diffusion potential and two Donnan potentials. The diffusion potential can be calculated by proceeding from equation (37). 

W. F. Graydon and R. J. Stewart (41) also compared the membrane potentials with the values according to equation (46). The membrane investigated was a copolymer of p-styrene sulfonic acid and styrene crosslinked with divinyl benzene. In the large majority of cases the experimental values were lower than those according to equation (46). The smaller part of this difference could be attributed to the transport of the co-ions and was calculated roughly. The greater part was attributed to water transport. From this the transport number of water was calculated it varied from 1 to about 60. It was found that the water transport was proportional to the water content and inversely proportional to the number of crosslinks. A provisional direct measurement was effected of a water transport number. The value corresponded rather well with the indirect determination as described above. 

For comparison of the SWV responses provided for systems of one and two polarized interfaces, Fig. 7.23 shows the/sw — E curves corresponding to the direct and to the reverse scans (solid line and empty circles, respectively) for both kinds of membrane systems, calculated for sw = 50 mV by using Eq. (7.44). The peaks obtained when two polarized interfaces are considered are shifted 8 mV with respect to those obtained for a system with a single polarized one, which implies that the half-wave potential for the system with two polarized interfaces can be easily determined from the peak potential by... 

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